A bag has 6 red, 2 blue and 4 yellow marbles. One marble is picked…

Step by step

The question

Question: A bag has 6 red, 2 blue and 4 yellow marbles.

One marble is picked without looking.

What is the probability it is yellow?

There are four choices.

First we solve it, the normal way.

Then we pick.

The probability is a fraction: the outcomes we want, over all the outcomes.

P stands for probability.

1 Count all outcomes

6 red.

2 blue.

4 yellow.

So there are 12 marbles in all.

6 plus 2 plus 4 is 12.

2 Count the ones we want

The yellow marbles: 4.

That is 4 outcomes we want.

3 Write the fraction

4 we want, out of 12.

So the probability is 4/12.

Careful!

The bottom is all the outcomes, 12.

Not only the other 8.

4 Simplify

Both 4 and 12 can be divided by 4.

That makes it simpler.

So it is 1/3.

5 As a percent

Percent means out of 100.

1/3 means 1 divided by 3.

Then times 100.

To the nearest tenth, that is about 33.3%.

6 Check

Let's check with the others.

12 minus 4 is 8.

4/12 plus 8/12 is 12/12: that is 1, all of them.

So the answer is right!

7 Pick the choice

Our answer is P(yellow) = 1/3.

That is choice B.

8 Why not the others

A is 1/12.

Wrong: 1 out of 12: there are 4 yellow marbles.

C is 1/2.

Wrong: 4 out of the 8 that are not yellow: the bottom is all 12 marbles.

That is the Careful mistake from before.

D is 2/3.

Wrong: that is the chance it is not yellow.

Let's look back.

First: count all outcomes.

Then: count the ones we want.

Then: write the fraction.

Then: simplify.

Then: as a percent.

Then: check.

Then: pick the choice.

Last: why not the others.